The fifth-grade curriculum presents many opportunities to use students' prior mathematical knowledge as a way to bridge new and more difficult mathematical ideas. In this article, the authors document an area tiling task given to fifth-grade students to connect aspects of area measurement covered in earlier grades to grade-level standards such as:…

Modeling is an effective tool to help students access mathematical concepts. Finding a math teacher who has not drawn a fraction bar or pie chart on the board would be difficult, as would finding students who have not been asked to draw models and represent numbers in different ways. In this article, the authors will discuss: (1) the properties of…

The authors explore how one teacher uses play and enacts the Effective Teaching Practices as a way to increase student engagement and autonomy and to meet learning goals when teaching mathematics with interactive simulations.

The author wants her students to see any new mathematics--fractions, negative numbers, algebra--as logical extensions of what they already know. This article describes two students' efforts to make sense of their conflicting interpretations of 1/2 × -6, both of which were compelling and logical to them. It describes how discussion, constructing…

As a group of middle school mathematics teachers and teacher educators, the authors have focused their attention on using innovative practices coupled with high cognitive demand tasks to engage students, pique their interest in mathematics, and promote conceptual understanding. This article explores their three-act task design. In act 1, students…

Mathematical modeling, a practice standard in the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010), is a process by which students develop and use mathematics as a tool to make sense of the world around them. Students investigate a real-world situation by asking mathematical questions; along the way, they need to decide how to use…

Engineering-based modeling activities provide a rich source of meaningful situations that capitalize on and extend students' routine learning. By integrating such activities within existing curricula, students better appreciate how their school learning in mathematics and science applies to problems in the outside world. Furthermore, modeling…

With the rise of personal desktop 3D printing, a wide spectrum of educational opportunities has become available for educators to leverage this technology in their classrooms. Until recently, the ability to create physical 3D models was well beyond the scope, skill, and budget of many schools. However, since desktop 3D printers have become readily…

Mathematics interventions for struggling students supplement regular instruction and are frequently implemented through computer programs and activity sheet practice (Swanson et al. 2012). However, students with foundational misunderstandings do not benefit from additional drill and practice alone. Instead, interventions that balance concepts with…

Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…

In the buzzing activity of the mathematics classroom, teaching in a way that effectively responds to and furthers students' thinking can be quite challenging. Given that teachers' instructional decisions will directly influence students' learning, it is extremely important to develop the sorts of practices that lead to productive in-the-moment…

Many current and future teachers have little experience with modeling and how to integrate it into their teaching. However, with the introduction of the Common Core State Standards for Mathematics (CCSSM) and its emphasis on mathematical modeling in all grades (CCSSI 2010), this integration has become paramount. Therefore, middle-grades teachers…

Mathematical modeling, a focus of the Common Core State Standards for School Mathematics (CCSSI 2010) and one of the Standards for Mathematical Practice, is generally considered to be the process of exploring a real-world situation and making sense of it using mathematics (Lesh and Zawojewski 2007). Teachers need to create opportunities for…

An important question for mathematics teachers is this: "How can we help students learn mathematics to solve everyday problems, rather than teaching them only to memorize rules and practice mathematical procedures?" Teaching students using modeling activities can help them learn mathematics in real-world problem-solving situations that…

The authors asked fifth-grade and eighth-grade students to pose stories for number sentences involving the addition and subtraction of integers. In this article, the authors look at eight stories from students. Which of these stories works for the given number sentence? What do they reveal about student thinking? When the authors examined these…